You can enter the distribution amounts on your tax return and let TurboTax calculate your tax due and use that amount as an estimate to pay now. Then later, when you get the K-1, go back and edit the amounts in TurboTax and file your actual return then.
If you have not filed an extension yet, you can do it from TurboTax or use the link in the informative article (at the bottom). This article also has a link to TaxCaster which can also help you estimate your taxes. How
Do I Get an Extension on Taxes?
Direct extension link - https://turbotax.intuit.com/irs-tax-extensions/